The El-Rewini/Ali Scheduling of In-Forest Task Graph on Two

Processors with Communication

Project Presentation

By David Y. Feinstein

SMU - CSE 8388 Spring 2005 Instructor: Dr. H. El-Rewini

April 25, 2005

Problem description An in-forest task graph allows only one successor task for each node. Out-forest task graphs are reversed. The Hu Scheduling algorithm (1961) of in/out-forest task graphs on arbitrary number of processor assumes no communication cost. The El-Rewini/Ali algorithm (1994) was the first to achieve optimal scheduling of in/out-forest tasks graph with communication. It does limit the maximum number of processors to two. The El-Rewini/Ali algorithm introduced the notion of Augmental Graph to compensate for the communication cost. The Augmental Graph can be scheduled using the Hu algorithm followed by the SwapAll check to verify or correct the resulting schedule.

My proposed solution This project provided an advanced framework to

simulate both Hu algorithm (on arbitrary number of processors) and the El-Rewini/Ali algorithm.

User can create, edit and store task graphs using node and successor arc editors.

After the required algorithm is selected, the user can animate the process of the GANTT diagram creation.

Augmental graph creation is show in the detailed algorithm output memo control. Sibling analysis results can be seen graphically.

My project currently supports only the In-Forest – it can be easily extended for Out-Forest task graphs.

Assumptions

Execution time of all tasks takes is one unit of time. Communication (in the El-Rewini/Ali algorithm) tasks

one unit of time. Since the program currently supports only In-Forest

task graphs, all successor arcs are pointing downward. (Arrow heads not shown for graph clarity)

The file extension name for this project is “*.eas” (for El-Rewini Ali Scheduling)

Overview

In-Forest Task Graph Creation

The user first generates the empty graph, after setting the number of levels.

Use Node Insert/Delete set the proper number of nodes

Use the successor editor to set the successor

Here is a sample of graph (also stored in “test1.eas”)

The Default Process Setup Selection is the El-Rewini/Ali optimal algorithm with Communication.

The El-Rewini/Ali Algorithm is the default. Number of processor is automatically set to 2 Must have a created graph (or a graph file *.eas

open).

The Hu Algorithm is Limited to No Communication

When selecting the “Hu Only” process, the Hu algorithm will run without communication.

You can set any number of processors. Users can simulate homework 4 Problem 10-1

(using file “test2.eas”)

The Augmental Graph Creation is an Essential Step of El-Rewini/Ali Algorithm

The Augmental Graph process performs sibling analysis in the algorithm output screen.

The use can select the “Show Sibling in Graph” or “Show Augmental Graph.

This partial display shows the detail algorithm output box

Other portions of the display show the Sibling Analysis and the Graph creation process.

Selecting “Show Sibling in Graph”

Selecting “Show Augmental Graph”

Notice what happens if we do not select “minimize arc crossing”. The result is still correct…

Hu Scheduling Control

You can use animation or single step. The Hu Scheduling animation can be shown on the

GANTT diagram or even on the graph itself. For El-Rewini/Ali, the Hu process works on the

Augmental Graph.

During the Hu animation, Done nodes are in read, Ready nodes are shown in Green.

Gantt Diagram and program output listing details

The Final process in the El-Rewini/Ali is checking the resulting Hu Schedule. The program performs the SwapAll operation if required.

Homework 4 problem 10-7 can be verified with the file test2.eas

File “test1.eas” required one swapall operation at time-6

Conclusions

The El-Rewini/Ali Augmental Graph was a critical and elegant inventive step in order to solve the problem of scheduling in-forest task graphs with communication.

Computation cost for the Augmental Graph creation are relatively minimal.

When using the Hu Only (without communications - not show on the slides but can be run on the program) – we quickly reach a point where adding processors do not increase the output.